Parallelogram Side Length: Finding Missing Side Given 20cm and 60cm Perimeter

Q: Why do we use 2(a + b) instead of adding all four sides?

In a parallelogram, opposite sides are always equal! So if one side is 20 cm, the opposite side is also 20 cm. This means we only need to find two different side lengths.

Q: What if I accidentally used all four sides in my calculation?

You might set up something like 20 + x + 20 + y = 60, but this creates two unknowns! Remember: opposite sides are equal, so x = 20 and y = the unknown side.

Q: Can a parallelogram have all sides equal?

Yes! When all four sides are equal, it's called a rhombus. But in this problem, we have different side lengths (20 cm and 10 cm), so it's a regular parallelogram.

Q: What if my answer doesn't make sense?

Always check that your answer is positive and reasonable! If you get a negative length or something much larger than the given side, double-check your algebra steps.

Parallelogram Perimeter with Unknown Side

A parallelogram has a perimeter of 60 cm.

AB = 20 cm

Calculate the length of the other side.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find AC

00:03 Opposite sides are equal in parallelograms

00:17 They are also a pair of opposite sides therefore equal

00:26 The perimeter of the parallelogram equals the sum of its sides

00:37 Let's substitute appropriate values and solve for BD

00:57 Let's group the numbers into one factor, and BD

01:07 Let's isolate BD

01:22 This is the length of BD

01:29 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A parallelogram has a perimeter of 60 cm.

AB = 20 cm

Calculate the length of the other side.

Step-by-step solution

To solve this problem, we'll use the perimeter formula for a parallelogram, which is:

$P = 2(a + b)$

where $P$ is the perimeter, $a$ is the length of one side, and $b$ is the length of the adjacent side.

Given:

Perimeter, $P = 60 \, \text{cm}$
One side, $AB = 20 \, \text{cm}$

Let's apply these values to the formula:

$60 = 2(20 + b)$

To isolate $b$ , we first divide both sides by 2:

$30 = 20 + b$

Now, solve for $b$ by subtracting 20 from both sides:

$b = 10 \, \text{cm}$

Therefore, the length of the other side is 10 cm.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perimeter Formula: For parallelograms, $P = 2(a + b)$ where opposite sides equal
Technique: Substitute known values: 60 = 2(20 + b), then solve algebraically
Check: Verify: 2(20 + 10) = 2(30) = 60 cm perimeter ✓

Common Mistakes

Avoid these frequent errors

Using regular rectangle perimeter formula
Don't add all four sides as separate unknowns = overcomplicated problem! This ignores that opposite sides are equal in parallelograms. Always use P = 2(a + b) where a and b are adjacent sides.

Practice Quiz

Test your knowledge with interactive questions

Given the parallelogram:

Calculate the perimeter of the parallelogram.

FAQ

Everything you need to know about this question

Why do we use 2(a + b) instead of adding all four sides?

In a parallelogram, opposite sides are always equal! So if one side is 20 cm, the opposite side is also 20 cm. This means we only need to find two different side lengths.

What if I accidentally used all four sides in my calculation?

You might set up something like 20 + x + 20 + y = 60, but this creates two unknowns! Remember: opposite sides are equal, so x = 20 and y = the unknown side.

How do I know which sides are opposite to each other?

In parallelogram ABCD, side AB is opposite to side CD, and side BC is opposite to side AD. Opposite sides never touch - they're parallel and equal in length.

Can a parallelogram have all sides equal?

Yes! When all four sides are equal, it's called a rhombus. But in this problem, we have different side lengths (20 cm and 10 cm), so it's a regular parallelogram.

What if my answer doesn't make sense?

Always check that your answer is positive and reasonable! If you get a negative length or something much larger than the given side, double-check your algebra steps.

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